-
A. Kruckenhauser, R. van Bijnen, T. Zache, M. Di Liberto, P. Zoller High-dimensional SO(4)-symmetric Rydberg manifolds for quantum simulation,
Quantum Sci. Technol. 8 (2022-12-19),
http://dx.doi.org/10.1088/2058-9565/aca996 doi:10.1088/2058-9565/aca996 (ID: 720885)
Toggle Abstract
We develop a toolbox for manipulating arrays of Rydberg atoms prepared in high-dimensional hydrogen-like manifolds in the regime of linear Stark and Zeeman effect. We exploit the SO(4) symmetry to characterize the action of static electric and magnetic fields as well as microwave and optical fields on the well-structured manifolds of states with principal quantum number n. This enables us to construct generalized large-spin Heisenberg models for which we develop state-preparation and readout schemes. Due to the available large internal Hilbert space, these models provide a natural framework for the quantum simulation of Quantum Field Theories, which we illustrate for the case of the sine-Gordon and massive Schwinger models. Moreover, these high-dimensional manifolds also offer the opportunity to perform quantum information processing operations for qudit-based quantum computing, which we exemplify with an entangling gate and a state-transfer protocol for the states in the neighborhood of the circular Rydberg level.
-
M. Meth, V. Kuzmin, Rick van Bijnen, L. Postler, R. Stricker, Rainer Blatt, M. Ringbauer, Thomas Monz, Pietro Silvi, Philipp Schindler Probing phases of quantum matter with an ion-trap tensor-network quantum eigensolver,
Phys. Rev. X 12 41035 (2022-03-28),
http://dx.doi.org/10.1103/PhysRevX.12.041035 doi:10.1103/PhysRevX.12.041035 (ID: 720826)
Toggle Abstract
Tensor-Network (TN) states are efficient parametric representations of ground states of local quantum Hamiltonians extensively used in numerical simulations. Here we encode a TN ansatz state directly into a quantum simulator, which can potentially offer an exponential advantage over purely numerical simulation. In particular, we demonstrate the optimization of a quantum-encoded TN ansatz state using a variational quantum eigensolver on an ion-trap quantum computer by preparing the ground states of the extended Su-Schrieffer-Heeger model. The generated states are characterized by estimating the topological invariants, verifying their topological order. Our TN encoding as a trapped ion circuit employs only single-site addressing optical pulses - the native operations naturally available on the platform. We reduce nearest-neighbor crosstalk by selecting different magnetic sublevels with well-separated transition frequencies to encode even and odd qubits.
-
C. Dlaska, K. Ender, G. B. Mbeng, A. Kruckenhauser, W. Lechner, R. van Bijnen Quantum optimization via four-body Rydberg gates,
Phys. Rev. Lett. 128 (2022-03-24),
http://dx.doi.org/10.1103/PhysRevLett.128.120503 doi:10.1103/PhysRevLett.128.120503 (ID: 720749)
Toggle Abstract
There is a large ongoing research effort towards obtaining a quantum advantage in the solution of combinatorial optimization problems on near-term quantum devices. A particularly promising platform for testing and developing quantum optimization algorithms are arrays of trapped neutral atoms, laser-coupled to highly excited Rydberg states. However, encoding combinatorial optimization problems in atomic arrays is challenging due to the limited inter-qubit connectivity given by their native finite-range interactions. Here we propose and analyze a fast, high fidelity four-body Rydberg parity gate, enabling a direct and straightforward implementation of the Lechner-Hauke-Zoller (LHZ) scheme and its recent generalization, the parity architecture, a scalable architecture for encoding arbitrarily connected interaction graphs. Our gate relies on onetime-optimized adiabatic laser pulses and is fully programmable by adjusting two hold-times during operation. We numerically demonstrate an implementation of the quantum approximate optimization algorithm (QAOA) for a small scale test problem. Our approach allows for efficient execution of variational optimization steps with a constant number of system manipulations, independent of the system size, thus paving the way for experimental investigations of QAOA beyond the reach of numerical simulations.
-
C. Marciniak, T. Feldker, I. Pogorelov, C. R. Kaubrügger, D. Vasilyev, R. van Bijnen, P. Schindler, P. Zoller, R. Blatt, T. Monz Optimal metrology with variational quantum circuits on trapped ions,
Nature 603 604 (2022-03-23),
http://dx.doi.org/10.1038/s41586-022-04435-4 doi:10.1038/s41586-022-04435-4 (ID: 720667)
Toggle Abstract
Cold atoms and ions exhibit unparalleled performance in frequency metrology epitomized in the atomic clock. More recently, such atomic systems have been used to implement programmable quantum computers and simulators with highest reported operational fidelities across platforms. Their strength in metrology and quantum information processing offers the opportunity to utilize tailored, programmable entanglement generation to approach the `optimal quantum sensor' compatible with quantum mechanics. Here we report quantum enhancement in metrology beyond squeezing through low-depth, variational quantum circuits searching for optimal input states and measurement operators in a trapped ion platform. We perform entanglement-enhanced Ramsey interferometry finding optimal parameters for variational quantum circuits using a Bayesian approach to stochastic phase estimation tailored to the sensor platform capabilities and finite dynamic range of the interferometer. We verify the performance by both directly using theory predictions of optimal parameters, and performing online quantum-classical feedback optimization to `self-calibrate' the variational parameters. In both cases we find that variational circuits outperform classical and direct spin squeezing strategies under realistic noise and imperfections. With 26 ions we achieve 2.02(8) dB of metrological gain over classical interferometers.
-
S. Hollerith, S. Srakaew, D. Wei, A. Rubio López, D. Adler, P. Weckesser, A. Kruckenhauser, V. Walther, R. van Bijnen, J. Rui, C. Gross, I. Bloch, J. Zeiher Realizing distance-selective interactions in a Rydberg-dressed atom array,
Phys. Rev. Lett. 128 113602 (2022-03-14),
http://dx.doi.org/10.1103/PhysRevLett.128.113602 doi:10.1103/PhysRevLett.128.113602 (ID: 720748)
Toggle Abstract
Measurement-based quantum computing relies on the rapid creation of large-scale entanglement in a register of stable qubits. Atomic arrays are well suited to store quantum information, and entanglement can be created using highly-excited Rydberg states. Typically, isolating pairs during gate operation is difficult because Rydberg interactions feature long tails at large distances. Here, we engineer distance-selective interactions that are strongly peaked in distance through off-resonant laser coupling of molecular potentials between Rydberg atom pairs. Employing quantum gas microscopy, we verify the dressed interactions by observing correlated phase evolution using many-body Ramsey interferometry. We identify atom loss and coupling to continuum modes as a limitation of our present scheme and outline paths to mitigate these effects, paving the way towards the creation of large-scale entanglement.
-
A. Rath, R. van Bijnen, A. Elben, P. Zoller, B. Vermersch Importance sampling of randomized measurements for probing entanglement,
Phys. Rev. Lett. 127 (2021-11-11),
http://dx.doi.org/10.1103/PhysRevLett.127.200503 doi:10.1103/PhysRevLett.127.200503 (ID: 720632)
Toggle Abstract
We show that combining randomized measurement protocols with importance sampling allows for characterizing entanglement in significantly larger quantum systems and in a more efficient way than in previous work. A drastic reduction of statistical errors is obtained using classical techniques of machine-learning and tensor networks using partial information on the quantum state. In present experimental settings of engineered many-body quantum systems this effectively doubles the (sub-)system sizes for which entanglement can be measured. In particular, we show an exponential reduction of the required number of measurements to estimate the purity of product states and GHZ states.
-
C. Kokail, B. Sundar, T. Zache, A. Elben, B. Vermersch, M. Dalmonte, R. van Bijnen, P. Zoller Quantum Variational Learning of the Entanglement Hamiltonian,
Phys. Rev. Lett. 127 170501 (2021-10-22),
http://dx.doi.org/10.1103/PhysRevLett.127.170501 doi:10.1103/PhysRevLett.127.170501 (ID: 720649)
Toggle Abstract
Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically realized on the quantum device, serve as an efficient variational ansatz for a local EH. Optimal variational parameters are determined in a feedback loop, involving quench dynamics with the deformed Hamiltonian as a quantum processing step, and classical optimization. We simulate the protocol for the ground state of Fermi-Hubbard models in quasi-1D geometries, finding excellent agreement of the EH with Bisognano-Wichmann predictions. Subsequent on-device spectroscopy enables a direct measurement of the entanglement spectrum, which we illustrate for a Fermi Hubbard model in a topological phase.
-
D. Paulson, L. Dellantonio, J. Haase, A. Celi, A. Kan, A. Jena, C. Kokail, R. van Bijnen, K. Jansen, P. Zoller, C. A. Muschik Simulating 2D effects in lattice gauge theories on a quantum computer,
PRX Quantum 2 30334 (2021-08-25),
http://dx.doi.org/10.1103/PRXQuantum.2.030334 doi:10.1103/PRXQuantum.2.030334 (ID: 720526)
Toggle Abstract
Quantum computing is in its greatest upswing, with so-called noisy-intermediate-scale-quantum devices heralding the computational power to be expected in the near future. While the field is progressing toward quantum advantage, quantum computers already have the potential to tackle classically intractable problems. Here, we consider gauge theories describing fundamental-particle interactions. On the way to their full-fledged quantum simulations, the challenge of limited resources on near-term quantum devices has to be overcome. We propose an experimental quantum simulation scheme to study ground-state properties in two-dimensional quantum electrodynamics (2D QED) using existing quantum technology. Our protocols can be adapted to larger lattices and offer the perspective to connect the lattice simulation to low-energy observable quantities, e.g., the hadron spectrum, in the continuum theory. By including both dynamical matter and a nonminimal gauge-field truncation, we provide the novel opportunity to observe 2D effects on present-day quantum hardware. More specifically, we present two variational-quantum-eigensolver- (VQE) based protocols for the study of magnetic field effects and for taking an important first step toward computing the running coupling of QED. For both instances, we include variational quantum circuits for qubit-based hardware. We simulate the proposed VQE experiments classically to calculate the required measurement budget under realistic conditions. While this feasibility analysis is done for trapped ions, our approach can be directly adapted to other platforms. The techniques presented here, combined with advancements in quantum hardware, pave the way for reaching beyond the capabilities of classical simulations.
-
D. Petter, A. Patscheider, G. Natale, M. J. Mark, M. Baranov, R. van Bijnen, S. M. Roccuzzo, A. Recati, B. Blakie, D. Baillie, L. Chomaz, F. Ferlaino Bragg scattering of an ultracold dipolar gas across the phase transition from Bose-Einstein condensate to supersolid in the free-particle regime,
Phys. Rev. A 104 L011302 (2021-07-22),
http://dx.doi.org/10.1103/PhysRevA.104.L011302 doi:10.1103/PhysRevA.104.L011302 (ID: 720484)
Toggle Abstract
We present an experimental and theoretical study of the high-energy excitation spectra of a dipolar supersolid. Using Bragg spectroscopy, we study the scattering response of the system to a high-energy probe, enabling measurements of the dynamic structure factor. We experimentally observe a continuous reduction of the response when tuning the contact interaction from an ordinary Bose-Einstein condensate to a supersolid state. Yet the observed reduction is faster than the one theoretically predicted by the Bogoliubov-de-Gennes theory. Based on an intuitive semi-analytic model and real-time simulations, we primarily attribute such a discrepancy to the out-of-equilibrium phase dynamics, which although not affecting the system global coherence, reduces its response.
-
C. Kokail, R. van Bijnen, A. Elben, B. Vermersch, P. Zoller Entanglement Hamiltonian Tomography in Quantum Simulation,
Nature Phys. (2021-06-24),
http://dx.doi.org/10.1038/s41567-021-01260-w doi:10.1038/s41567-021-01260-w (ID: 720530)
Toggle Abstract
Entanglement is the crucial ingredient of quantum many-body physics, and characterizing and quantifying entanglement in closed system dynamics of quantum simulators is an outstanding challenge in today's era of intermediate scale quantum devices. Here we discuss an efficient tomographic protocol for reconstructing reduced density matrices and entanglement spectra for spin systems. The key step is a parametrization of the reduced density matrix in terms of an entanglement Hamiltonian involving only quasi local few-body terms. This ansatz is fitted to, and can be independently verified from, a small number of randomised measurements. The ansatz is suggested by Conformal Field Theory in quench dynamics, and via the Bisognano-Wichmann theorem for ground states. Not only does the protocol provide a testbed for these theories in quantum simulators, it is also applicable outside these regimes. We show the validity and efficiency of the protocol for a long-range Ising model in 1D using numerical simulations. Furthermore, by analyzing data from 10 and 20 ion quantum simulators [Brydges \textit{et al.}, Science, 2019], we demonstrate measurement of the evolution of the entanglement spectrum in quench dynamics.
-
L. R. Picard, M. J. Mark, F. Ferlaino, R. van Bijnen Deep Learning-Assisted Classification of Site-Resolved Quantum Gas Microscope Images,
Measurement Science and Technology 31 25201 (2019-11-05),
http://dx.doi.org/10.1088/1361-6501/ab44d8 doi:10.1088/1361-6501/ab44d8 (ID: 720262)
-
C. R. Kaubrügger, P. Silvi, C. Kokail, R. van Bijnen, A. M. Rey, J. Ye, A. Kaufman, P. Zoller Variational spin-squeezing algorithms on programmable quantum sensors,
Phys. Rev. Lett. 123 260505 (2019-08-22),
http://dx.doi.org/10.1103/PhysRevLett.123.260505 doi:10.1103/PhysRevLett.123.260505 (ID: 720356)
Toggle Abstract
Arrays of atoms trapped in optical tweezers combine features of programmable analog quantum simulators with atomic quantum sensors. Here we propose variational quantum algorithms, tailored for tweezer arrays as programmable quantum sensors, capable of generating entangled states on-demand for precision metrology. The scheme is designed to generate metrological enhancement by optimizing it in a feedback loop on the quantum device itself, thus preparing the best entangled states given the available quantum resources. We apply our ideas to generate spin-squeezed states on Sr atom tweezer arrays, where finite-range interactions are generated through Rydberg dressing. The complexity of experimental variational optimization of our quantum circuits is expected to scale favorably with system size. We numerically show our approach to be robust to noise, and surpassing known protocols.
-
G. Natale, R. van Bijnen, A. Patscheider, D. Petter, M. J. Mark, L. Chomaz, F. Ferlaino Excitation spectrum of a trapped dipolar supersolid and its experimental evidence,
Phys. Rev. Lett. 123 50402 (2019-08-01),
http://dx.doi.org/10.1103/PhysRevLett.123.050402 doi:10.1103/PhysRevLett.123.050402 (ID: 720313)
Toggle Abstract
We study the spectrum of elementary excitations of a trapped dipolar Bose gas across the superfluid-supersolid phase transition. Our calculations, accounting for the experimentally relevant case of confined systems, show that, when entering the supersolid phase, two distinct excitation branches appear, respectively connected to crystal or superfluid orders. These results confirm infinite-system predictions, showing that finite-size effects play only a small qualitative role. Experimentally, we probe compressional excitations in an Er quantum gas across the phase diagram. While in the BEC regime the system exhibits an ordinary quadrupole oscillation, in the supersolid regime, we observe a striking two-frequency response of the system, related to the two spontaneously broken symmetries.
-
C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, P. Jurcevic, C. A. Muschik, P. Silvi, R. Blatt, C. F. Roos, P. Zoller Self-verifying variational quantum simulation of lattice models,
Nature 569 360 (2019-05-15),
http://dx.doi.org/10.1038/s41586-019-1177-4 doi:10.1038/s41586-019-1177-4 (ID: 720076)
Toggle Abstract
Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments demonstrating self-verifying, hybrid, variational quantum simulation of lattice models in condensed matter and high-energy physics. Contrary to analog quantum simulation, this approach forgoes the requirement of realising the targeted Hamiltonian directly in the laboratory, thus allowing the study of a wide variety of previously intractable target models. Here, we focus on the Lattice Schwinger model, a gauge theory of 1D quantum electrodynamics. Our quantum co-processor is a programmable, trapped-ion analog quantum simulator with up to 20 qubits, capable of generating families of entangled trial states respecting symmetries of the target Hamiltonian. We determine ground states, energy gaps and, by measuring variances of the Schwinger Hamiltonian, we provide algorithmic error bars for energies, thus addressing the long-standing challenge of verifying quantum simulation.
-
D. Petter, G. Natale, R. van Bijnen, A. Patscheider, M. J. Mark, L. Chomaz, F. Ferlaino Probing the roton excitation spectrum of a stable dipolar Bose gas,
Phys. Rev. Lett. 122 183401 (2019-05-08),
http://dx.doi.org/10.1103/PhysRevLett.122.183401 doi:10.1103/PhysRevLett.122.183401 (ID: 720098)
Toggle Abstract
We measure the excitation spectrum of a stable dipolar Bose--Einstein condensate over a wide momentum-range via Bragg spectroscopy. We precisely control the relative strength, εdd, of the dipolar to the contact interactions and observe that the spectrum increasingly deviates from the linear phononic behavior for increasing εdd. Reaching the dipolar dominated regime εdd>1, we observe the emergence of a roton minimum in the spectrum and its softening towards instability. We characterize how the excitation energy and the strength of the density-density correlations at the roton momentum vary with εdd. Our findings are in excellent agreement with numerical calculations based on mean-field Bogoliubov theory. When including beyond-mean-field corrections, in the form of a Lee-Huang-Yang potential, we observe a quantitative deviation from the experiment, questioning the validity of such a description in the roton regime.
-
L. Chomaz, D. Petter, P. Ilzhöfer, G. Natale, A. Trautmann, C. Politi, G. Durastante, R. van Bijnen, A. Patscheider, M. Sohmen, M. J. Mark, F. Ferlaino Long-Lived and Transient Supersolid Behaviors in Dipolar Quantum Gases,
Phys. Rev. X 9 21012 (2019-04-19),
http://dx.doi.org/10.1103/PhysRevX.9.021012 doi:10.1103/PhysRevX.9.021012 (ID: 720203)
Toggle Abstract
By combining theory and experiments, we demonstrate that dipolar quantum gases of both 166Er and 164Dy support a state with supersolid properties, where a spontaneous density modulation and a global phase coherence coexist. This paradoxical state occurs in a well defined parameter range, separating the phases of a regular Bose-Einstein condensate and of an insulating droplet array, and is rooted in the roton mode softening, on the one side, and in the stabilization driven by quantum fluctuations, on the other side. Here, we identify the parameter regime for each of the three phases. In the experiment, we rely on a detailed analysis of the interference patterns resulting from the free expansion of the gas, quantifying both its density modulation and its global phase coherence. Reaching the phases via a slow interaction tuning, starting from a stable condensate, we observe that 166Er and 164Dy exhibit a striking difference in the lifetime of the supersolid properties, due to the different atom loss rates in the two systems. Indeed, while in 166Er the supersolid behavior only survives a few tens of milliseconds, we observe coherent density modulations for more than 150ms in 164Dy. Building on this long lifetime, we demonstrate an alternative path to reach the supersolid regime, relying solely on evaporative cooling starting from a thermal gas.
-
J. Zeiher, J. Choi, A. Rubio Abadal, T. Pohl, R. van Bijnen, I. Bloch, C. Gross Coherent many-body spin dynamics in a long-range interacting Ising chain,
Phys. Rev. X 7 41063 (2017-12-14),
http://dx.doi.org/10.1103/PhysRevX.7.041063 doi:10.1103/PhysRevX.7.041063 (ID: 719831)
Toggle Abstract
Coherent many-body quantum dynamics lies at the heart of quantum simulation and quantum computation. Both require coherent evolution in the exponentially large Hilbert space of an interacting many-body system. To date, trapped ions have defined the state of the art in terms of achievable coherence times in interacting spin chains. Here, we establish an alternative platform by reporting on the observation of coherent, fully interaction-driven quantum revivals of the magnetization in Rydberg-dressed Ising spin chains of atoms trapped in an optical lattice. We identify partial many-body revivals at up to about ten times the characteristic time scale set by the interactions. At the same time, single-site-resolved correlation measurements link the magnetization dynamics with inter-spin correlations appearing at different distances during the evolution. These results mark an enabling step towards the implementation of Rydberg atom based quantum annealers, quantum simulations of higher dimensional complex magnetic Hamiltonians, and itinerant long-range interacting quantum matter.
(local copy)
-
J. Cui, R. van Bijnen, T. Pohl, S. Montangero, T. Calarco Optimal control of Rydberg lattice gases,
Quantum Sci. Technol. 2 35006 (2017-08-02),
http://dx.doi.org/10.1088/2058-9565/aa7daf doi:10.1088/2058-9565/aa7daf (ID: 719830)
Toggle Abstract
We present optimal control protocols to prepare different many-body quantum states of Rydberg atoms in optical lattices. Specifically, we show how to prepare highly ordered many-body ground states, GHZ states as well as some superposition of symmetric excitation number Fock states, that inherit the translational symmetry from the Hamiltonian, within sufficiently short excitation times minimizing detrimental decoherence effects. For the GHZ states, we propose a two-step detection protocol to experimentally verify the optimal preparation of the target state based only on standard measurement techniques. Realistic experimental constraints and imperfections are taken into account by our optimization procedure making it applicable to ongoing experiments.
(local copy)
-
A. Glätzle, R. van Bijnen, P. Zoller, W. Lechner A Coherent Quantum Annealer with Rydberg Atoms,
Nat. Commun. 8 15813 (2017-06-22),
http://dx.doi.org/10.1038/ncomms15813 doi:10.1038/ncomms15813 (ID: 719686)
Toggle Abstract
There is a significant ongoing effort in realizing quantum annealing with different physical platforms. The challenge is to achieve a fully programmable quantum device featuring coherent adiabatic quantum dynamics. Here we show that combining the well-developed quantum simulation toolbox for Rydberg atoms with the recently proposed Lechner-Hauke-Zoller~(LHZ) architecture allows one to build a prototype for a coherent adiabatic quantum computer with all-to-all Ising interactions and, therefore, a novel platform for quantum annealing. In LHZ a infinite-range spin-glass is mapped onto the low energy subspace of a spin-1/2 lattice gauge model with quasi-local 4-body parity constraints. This spin model can be emulated in a natural way with Rubidium and Cesium atoms in a bipartite optical lattice involving laser-dressed Rydberg-Rydberg interactions, which are several orders of magnitude larger than the relevant decoherence rates. This makes the exploration of coherent quantum enhanced optimization protocols accessible with state-of-the-art atomic physics experiments.
(local copy)